More details will be provided in a forthcoming paper by F. Russo and G. Staglianò.
i1 : X = specialFourfold random({5:{1}},0_(PP_(ZZ/33331)^7));
o1 : ProjectiveVariety, complete intersection of three quadrics in PP^7 containing a surface of degree 1 and sectional genus 0
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i2 : describe X
o2 = Complete intersection of 3 quadrics in PP^7
of discriminant 31 = det| 8 1 |
| 1 4 |
containing a surface of degree 1 and sectional genus 0
cut out by 5 hypersurfaces of degree 1
(This is a classical example of rational fourfold)
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i3 : time U' = associatedCastelnuovoSurface X;
-- used 5.93437s (cpu); 2.21093s (thread); 0s (gc)
o3 : ProjectiveVariety, Castelnuovo surface associated to X
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i4 : (mu,U,C,f) = building U';
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i5 : ? mu
o5 = multi-rational map consisting of one single rational map
source variety: 5-dimensional subvariety of PP^7 cut out by 2 hypersurfaces of degree 2
target variety: PP^4
dominance: true
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